# Seminario di Probabilità e Finanza Matematica: On the stochastic Fourier transformation and its invertibility

## Venerdì 12 Luglio, ore 11:30 - Aula seminari VII piano - Shigeyoshi Ogawa

ARGOMENTI: Seminari

Seminario di Probabilità e Finanza Matematica

Venerdì 12 Luglio alle ore 11:30 nell'aula seminari al VII piano il Prof. Shigeyoshi Ogawa della Ritsumeikan University (Giappone) terrà un seminario intitolato: "On the stochastic Fourier transformation and its invertibility"

Abstract
For a square integrable random function $f(t,omega)$ and an orthonormal basis ${varphi_n(t)}$ in $L^2(0,1)$ the author introduced a stochastic Fourier transformation via its stochastic Fourier coefficients which are defined by the stochastic integral with respect to the Brownian motion, $int_0^1 varphi_n(t)f(t,omega)dW_t$.
It was shown in earlier articles (eg.[1]) that the transformation plays an essential role in the study of linear stochastic integral equations, but many questions are still left open.
In this talk we discuss the question of invertibility of the transformation and show some recent results ([2],[3]) as well as possible applications to mathematical sciences like volatility estimation.

References:
[1] S.Ogawa; "On a stochastic integral equation for the random fields", Seminaires de Proba., vol.25, 1991, Springer-Verlag
[2] S.Ogawa; "On a stochastic Fourier transformation", Stochastics Vol. 85, issue 2, 2013
[3] S.Ogawa and H.Uemura; "On a stochastic Fourier coefficient" (to appear) in J.Theor.Proba., (2013)